We focus our attention to the set Gr（ξ） of grouplike elements of a coring ξover a ring A. We do some observations on the actions of the groups U（A） and Aut（ξ~） of units of A and of automorphisms of corings of...We focus our attention to the set Gr（ξ） of grouplike elements of a coring ξover a ring A. We do some observations on the actions of the groups U（A） and Aut（ξ~） of units of A and of automorphisms of corings of ξ, respectively, on Gr（ξ）, and on the subset Gal（ξ）of all Galois grouplike elements. Among them, we give conditions on ξ under which Gal（ξ） is a group, in such a way that there is an exact sequence of groups {1} → U（Ag） → U（A） → Gal（ξ） → {1}, where Ag is the subalgebra of coinvaxiants for some g ∈ Gal（ξ）.展开更多
基金Supported by grant MTM2007-61673 from the Ministerio de Educación y Ciencia of SpainP06-FQM-01889 from Junta de Andalucía
文摘We focus our attention to the set Gr（ξ） of grouplike elements of a coring ξover a ring A. We do some observations on the actions of the groups U（A） and Aut（ξ~） of units of A and of automorphisms of corings of ξ, respectively, on Gr（ξ）, and on the subset Gal（ξ）of all Galois grouplike elements. Among them, we give conditions on ξ under which Gal（ξ） is a group, in such a way that there is an exact sequence of groups {1} → U（Ag） → U（A） → Gal（ξ） → {1}, where Ag is the subalgebra of coinvaxiants for some g ∈ Gal（ξ）.
